1. You open the page: Thermophysical Properties of Fluid Systems.
2. On this page you select Methane instead of Water, select needed for you units of measurement, and select the form of database, for example, Isothermal. Then you press to continue.
3.On the page Isothermal Properties for Methane you select temperature, for example, 300; select minimal, maximal pressure and increment, for example: 0 2 0.01
Do not forget to clean the box N3 with Java
4. Press for data
5. On the next page you will see a table with many properties, including JTC
6. To change the form and ranges of data you return back.

The Equation (14 ) follows from the van der Waals equation, that is good for overall picture, but is not precise in details. The Joule-Thomson coefficient is very sensitive to parameters of the intermolecular forces. Therefore, it is better to use direct experimental data, generalized in databases, like the NIST Database.